Emissions analyzers, or measurement instruments, measure certain gaseous constituents within a sample of exhaust, or aerosol, as a function of time, or are configured to measure particulate matter, such as soot, within an exhaust sample, as examples. The response of the instrument, however, may be uncorrected for the convolution of the measurement with some other signal representative of the transfer function, or the transient response, of the instrument. Deconvolution is a process used to reverse, or correct, the effects of convolution.
In one known method, the response of an instrument is recorded online in the time domain. Deconvolution of the recorded signal is performed offline in post-processing by (1) decomposing the recorded data, via a Fourier transform, into the frequency domain, (2) using a model to remove the effects convolution, and then (3) constructing a convolution corrected signal, via an inverse Fourier transform, back into the time domain.